Huh? Are you confusing the Philippines with Muslim-infested Indonesia or something? The Philippines are OVERWHELMINGLY Roman Catholic (more so than any existing American state) and the Muslims population is a small minority in single digits (around 5% of the population according to the last census). Methodists are 6% of the population of Illinois. So do we have a large influx of "Methodist Congressmen" in America thanks to Illinois having 18 seats in Congress, and a big "Methodist influence" in our state? Hardly.
My observation with Filipino-Americans, anyway, is all the ones I've met are pretty strongly pro-life Catholics and heavily lean Republican. Of course, the population living in the U.S. can't be identical to their equivalents on the island, but I wouldn't be surprised if Filipino-Americans were the most GOP friendly voting bloc of all Asian-Americans.
That being said, I'd absolutely oppose "statehood for the Philippines" for other reasons. For starters, they ceased being a US territory and severed ties with us decades ago. Secondly, as you noted, we'd have to absorb a huge, low income island population and that would be a terrible drain on the American economy. And the most obvious reason I'm against it -- I think its sheer insanity to some faraway island nation that has little in common the culture of the US mainland to become a state. It was a terrible idea when they did it for Hawaii, and it would be terrible for the Philippines.
5% (a minimum estimate, could be twice as much) of 100 million people is 5 million people, and they, unlike Methodists in Illinois, are concentrated in muzzie areas so they would get their own Congressional seats. Also unlike Methodists in Illinois, being Muslim is part of their political identity, and a large number of them are terrorist friendly.
Hawaiian statehood would have been fine, if not for the labor union coup in 1954. Oh what a paradise a GOP Hawaii would be.
Alaska also looked like a labor democrat disaster, but they wised up. Indeed if I’m not mistaken it was believed that of the 2, Alaska would be the more democrat state.